# The Value of Planning for Infinite-Horizon Model Predictive Control

arXiv: https://arxiv.org/abs/2104.02863 · HTML: https://mlsanity.com/paper/2104.02863/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 28 references that are in the map.
- First posted on arXiv 7 Apr 2021.

## Builds on (most cited first, 12 of 12)

- [Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm](https://mlsanity.com/paper/1712.01815/) (2017)
- [Solving Rubik's Cube with a Robot Hand](https://mlsanity.com/paper/1910.07113/) (2019)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [Thinking Fast and Slow with Deep Learning and Tree Search](https://mlsanity.com/paper/1705.08439/) (2017)
- [Emergence of Locomotion Behaviours in Rich Environments](https://mlsanity.com/paper/1707.02286/) (2017)
- [Plan Online, Learn Offline: Efficient Learning and Exploration via Model-Based Control](https://mlsanity.com/paper/1811.01848/) (2018)
- [Truncated Horizon Policy Search: Combining Reinforcement Learning & Imitation Learning](https://mlsanity.com/paper/1805.11240/) (2018)
- [Blending MPC & Value Function Approximation for Efficient Reinforcement Learning](https://mlsanity.com/paper/2012.05909/) (2020)
- [An Online Learning Approach to Model Predictive Control](https://mlsanity.com/paper/1902.08967/) (2019)
- [Information Theoretic Model Predictive Q-Learning](https://mlsanity.com/paper/2001.02153/) (2019)
- [Sampling-based Algorithms for Optimal Motion Planning Using Closed-loop Prediction](https://mlsanity.com/paper/1601.06326/) (2016)
- [Incremental Sampling-based Motion Planners Using Policy Iteration Methods](https://mlsanity.com/paper/1609.05960/) (2016)

## Built on by (most cited first, 8 of 8)

- [Temporal Difference Learning for Model Predictive Control](https://mlsanity.com/paper/2203.04955/) (2022)
- [Synthesis of Model Predictive Control and Reinforcement Learning: Survey and Classification](https://mlsanity.com/paper/2502.02133/) (2025)
- [Continuous Monte Carlo Graph Search](https://mlsanity.com/paper/2210.01426/) (2022)
- [Generative Models From and For Sampling-Based MPC: A Bootstrapped Approach For Adaptive Contact-Rich Manipulation](https://mlsanity.com/paper/2510.14643/) (2025)
- [Model Predictive Adversarial Imitation Learning for Planning from Observation](https://mlsanity.com/paper/2507.21533/) (2025)
- [Enhancing AUV Autonomy With Model Predictive Path Integral Control](https://mlsanity.com/paper/2308.05547/) (2023)
- [M3PC: Test-time Model Predictive Control for Pretrained Masked Trajectory Model](https://mlsanity.com/paper/2412.05675/) (2024)
- [Guided Riemannian Optimization (GuRO): Bridging Model Predictive Control and Decision Transformers](https://mlsanity.com/paper/2608.23204/) (2026)

## Abstract (arXiv)

Model Predictive Control (MPC) is a classic tool for optimal control of complex, real-world systems. Although it has been successfully applied to a wide range of challenging tasks in robotics, it is fundamentally limited by the prediction horizon, which, if too short, will result in myopic decisions. Recently, several papers have suggested using a learned value function as the terminal cost for MPC. If the value function is accurate, it effectively allows MPC to reason over an infinite horizon. Unfortunately, Reinforcement Learning (RL) solutions to value function approximation can be difficult to realize for robotics tasks. In this paper, we suggest a more efficient method for value function approximation that applies to goal-directed problems, like reaching and navigation. In these problems, MPC is often formulated to track a path or trajectory returned by a planner. However, this strategy is brittle in that unexpected perturbations to the robot will require replanning, which can be costly at runtime. Instead, we show how the intermediate data structures used by modern planners can be interpreted as an approximate value function. We show that that this value function can be used by MPC directly, resulting in more efficient and resilient behavior at runtime.